2.3 Assessing Pitch Quality
2.3.5 What is an average?
1 An average is a value which aims to represent a typical value for the range being looked at.
The average of the values within a range of values will be used to determine the overall grade for each performance standard. However, which average to use may need to change if a representative value is to be provided from an analysis.
We will take a quick look at the three different interpretations of an average before moving on.
2 Mean
The mean is the most common average value used and this is calculated by adding all the values together and then dividing by the number of values.
Example, if there are 10 values and these are 10, 10, 15, 40, 50, 35, 26, 28, 45, 51, then these all added together have a total of 310; this is then divided by the 10 instances, so the average is 310 / 10 = 31.
If, however, one or a few values are significantly different from the remainder then the average value might not be representative of any of the values, in which case this would not be a suitable one to use.
3 Median
The median is the middle value in the range when they are arranged in order. This is useful to use when outlier (more extreme) values are included within a wide range of data, which are not representative of the main values.
The median is useful when there is a wide range of values, as the dataset is divided into two halves and the median is the centre value. This is a more appropriate average to use when, for example, comparing incomes, average salaries, or house prices, especially when a lot of values are included within the dataset.
Where there are only a few values within a dataset then the median is a poor determinant for an average because it is often less representative of the data distribution and reliability of the central value can be significantly influenced by the addition or removal of a single value.
Where there are two middle values, when using an even number of values then the median is the average of those two values. Using the same figures as before, if there are 10 values and these are 10, 10, 15, 26, 28, 35, 40, 45, 50, 51, then the middle values are 28 and 35, so the average of these is 31.5.
4 Mode
The mode is another ‘average’ which is sometimes used. This is the value that appears most frequently. If there are two numbers, the average is said to be bimodal.
So, using the previous figures we see that 10 is the most common value. It would not be appropriate to use this ‘average’ in this example because it does not represent the central value of the data range.
The mode average might, for example, be useful for identifying the most common category of membership within an organisation.
5 Note: There are numerous online calculators for quickly determining these values; a useful one that is available at the time of writing is on Calculator Soup.